Integration questions in separably good characteristics

Let $G$ be a reductive group over an algebraically closed field $k$ of separably good characteristic $p>0$ for . Under these assumptions, Springer isomorphism $\phi : \mathcal {N}_{\mathrm {red}}(\mathfrak {g}) \rightarrow {V}_{\mathrm {red}}(G)$ from the nilpotent scheme $\mathfrak {g}$ to unipotent always exists and allows one integrate any $p$ -nilpotent element into One should wonder whether such punctual integration can lead restricted -nil -subalgebras {g}= \operatorname {Lie}(G)$ We provide counter-example existence in general, as well criteria some (that are maximal certain sense). This requires generalisation notion infinitesimal saturation first introduced by Deligne extension his theorems on infinitesimally saturated subgroups previously mentioned framework.